The "Axiomatic Method" and Its Constitutive Role in Physics

Using geometry as the primary example of the "axiomatic method", I will investigate the role of the axiomatic method in physics. I will argue that, while there are important parallels, there are also significant differences between the constitutive roles of the axiomatic method in the two disciplines. The main achievement of the axiomatic method in geometry is a sweeping clarification of the logical dependence and independence of the axioms with respect to each other. In physics, however, the main focuses of attention are the questions of the consistency of different assumptions from distinct fields and the "Lückenlosigkeit" of an alleged deduction of a central theorem like Boltzmann's equation.